AMP was derived based on the loopy BP with Gaussian and Taylor-series approximations [1]}, [2]}, which can be used to efficiently solve linear inverse problems due to its low complexity.
An issue with AMP is that it can easily diverge in the case of blacka generic measurement matrix, such as correlated, ill-conditioned, non-zero mean or rank-deficient \(\mathbf {A}\)  [3]}.
Inspired by the work in [4]}, it was shown in [5]} that the robustness of AMP is remarkably improved through simple pre-processing, i.e., performing a unitary transformation to the original linear model [5]}, [7]}.
As any matrix \(\mathbf {A}\)  has an SVD \(\mathbf {A= U \Lambda V}\)  with \(\mathbf {U}\)  and \(\mathbf {V}\)  being two unitary matrices, performing a unitary transformation with \(\mathbf {U}^H\)  leads to the following model
\(\mathbf {r=\Phi x}+\mathbf {\omega },\) 
